Question

In the given figure PQ || RS, TR || QU and $\angle PTR={42}^{\circ }$. Find $\angle QUR.$

Answer 1

Since, PQ and RS are parallel and TR is transversal,
Therefore,
$\angle PTR=\angle TRU\left[alternateinteriorangles\right]\Rightarrow \angle TRU={42}^{\circ }$
Now, TR is parallel to QU and RS is transversal.
Therefore, $\angle TRU+\angle RUQ={180}^{\circ }\left[consecutiveinteriorangles\right]\Rightarrow {42}^{\circ }+\angle RUQ={180}^{\circ }\Rightarrow \angle RUQ={180}^{\circ }-{42}^{\circ }={138}^{\circ }$